# US 9,435,200 B2 · Determination of thermodynamic properties of a fluid based on density and sound speed

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- Number: US 9,435,200 B2
- Document ID: US9435200B2
- Status: Granted
- Kind: B2
- Application number: 13/364,750
- Filed: 2012-02-02
- Published: 2013-08-08
- Granted: 2016-09-06
- Earliest claimed: 2012-02-02
- Assignees: Schlumberger Technology Corporation
- Applicants: Anthony Robert Holmes Goodwin
- Inventors: Anthony Robert Holmes Goodwin
- Web page: https://patentgrep.com/patent/US9435200B2

## CPC

- E21B 49/10: using side-wall fluid samplers or testers
- G01K 13/02: for measuring temperature of moving fluids or granular materials capable of flow
- G01K 17/06: Measuring quantity of heat conveyed by flowing media, e.g. in heating systems (G01K17/02, G01K17/04 take precedence){e.g. the quantity of heat in a transporting medium, delivered to or consumed in an expenditure device}
- G01N 25/18: by investigating thermal conductivity (by calorimetry G01N25/20; by measuring change of resistance of an electrically-heated body G01N27/18)
- E21B 49/0875: {determining specific fluid parameters}
- G06F 17/40: Data acquisition and logging (for input to computer G06F3/00)
- G16Z 99/00: Subject matter not provided for in other main groups of this subclass
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- G01K: MEASURING TEMPERATURE; MEASURING QUANTITY OF HEAT; THERMALLY-SENSITIVE ELEMENTS NOT OTHERWISE PROVIDED FOR (radiation pyrometry G01J5/00)
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G16Z: INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS, NOT OTHERWISE PROVIDED FOR

## Abstract

Variable volume systems and methods of use thereof described herein are capable of making calibrated determinations of fluid properties and phase behavior of a fluid sample. The determinations can be calibrated based on one or more calibration functions, such as system volume corrected for pressure and temperature variations. Cross-checking the results of measurements can be used to determine accuracy of the calibration or monitor for leaks or other anomalies of the variable volume systems. The variable volume systems can be implemented in a well logging tool and are capable of being calibrated downhole.

## Claims

### Claim 1

A system, comprising:
a fluid sample container that alters a temperature or a pressure of a fluid sample;
an optical fluid analyzer (OFA) that determines a compressibility of the fluid sample at each of a plurality of pressures or temperatures, wherein the compressibility comprises an isothermal compressibility κT or an isentropic compressibility κS, wherein the isothermal compressibility is defined by the equation
κ
T
=
-
1
V
⁢
(
∂
V
∂
p
)
T
and the isentropic compressibility is defined by the equation
κ
S
=
-
1
V
⁢
(
∂
V
∂
p
)
S
where V is volume, p is pressure, S is entropy, and T is temperature;
a sound speed component that measures a speed of sound in the fluid sample at each of the plurality of pressures or temperatures; and
an analysis component that calculates, at each of the plurality of pressures or temperatures, a density of the fluid sample based at least in part on the compressibility and the speed of sound, wherein the analysis component determines one or more thermodynamic properties of the fluid sample based at least in part on the density and the speed of sound, wherein the one or more thermodynamic properties comprises at least one of a property indicative of heat capacity of the fluid sample, a property indicative of an expansivity of the fluid sample, or a property indicative of an adiabatic index of the fluid sample.

### Claim 2 (depends on 1)

The system of claim 1, wherein the sound speed component comprises a sonic transducer and a pair of reflectors, and the sound speed component measures the speed of sound based at least in part on a travel time of a pair of sound pulses from the sonic transducer to the pair of reflectors and back to the sonic transducer.

### Claim 3 (depends on 1)

The system of claim 1, wherein the OFA measures the compressibility based at least in part on a determination of a change in the area under an absorption peak of a spectrum of the fluid sample.

### Claim 4 (depends on 1)

The system of claim 1, wherein the system is implemented at least in part in at least one of a logging while drilling tool or a measurement while drilling tool.

### Claim 5 (depends on 1)

The system of claim 1, wherein the system is implemented at least in part in a wireline tool.

### Claim 6 (depends on 1)

The system of claim 1, wherein the analysis component determines the one or more thermodynamic properties based at least in part on a numerical integration of the density and the speed of sound over a region of a pressure-temperature space.

### Claim 7 (depends on 6)

The system of claim 6, wherein the numerical integration is based on iteration of determinations of derivatives with respect to pressure of the density and a specific heat of the fluid sample, and estimation of the density and specific heat at a greater pressure based at least in part on the derivatives.

### Claim 8 (depends on 6)

The system of claim 6, wherein the analysis component represents the density and the speed of sound as polynomial functions with rational exponents.

### Claim 9 (depends on 8)

The system of claim 8, wherein the analysis component determines one or more parameters of the polynomial functions based at least in part on regression analysis.

### Claim 10

A method, comprising:
capturing a sample of a fluid;
determining, for each of a plurality of pressures in a range of pressures, a density, a speed of sound, and a heat capacity of the sample, comprising:
measuring the speed of sound in the sample for each of a plurality of temperatures in a range of temperatures;
determining a density for the sample for each of the plurality of temperatures, wherein determining the density comprises measuring a compressibility of the sample, the compressibility comprises an isothermal compressibility κT or an isentropic compressibility κS, wherein the isothermal compressibility is defined by the equation
κ
T
=
-
1
V
⁢
(
∂
V
∂
p
)
T
and the isentropic compressibility is defined by the equation
κ
S
=
-
1
V
⁢
(
∂
V
∂
p
)
S
where V is volume, p is pressure, S is entropy, and T is temperature; and
estimating the heat capacity of the sample for each of the plurality of temperatures; and
determining one or more thermodynamic properties based at least in part on the determined density, the speed of sound, and the heat capacity, wherein the one or more thermodynamic properties comprise at least one of a heat capacity of the sample, an expansivity of the sample, or an adiabatic index of the sample.

### Claim 11 (depends on 10)

The method of claim 10, wherein measuring the speed of sound comprises determining a travel time associated with at least one pulse sent from a transducer.

### Claim 12 (depends on 10)

The method of claim 10, wherein estimating the heat capacity comprises extrapolating the speed of sound and the density to at least one of pressure values outside the range of pressures or temperatures outside the range of temperatures.

### Claim 13 (depends on 10)

The method of claim 10, wherein determining, for each of a plurality of pressures, the density, the speed of sound, and the heat capacity of the sample is based at least in part on measurements taken by a wireline tool.

### Claim 14 (depends on 10)

The method of claim 10, wherein determining, for each of a plurality of pressures, the density, the speed of sound, and the heat capacity of the sample is based at least in part on measurements taken by one or more of a measurement while drilling (MWD) or logging while drilling (LWD) tool.

### Claim 15 (depends on 10)

The method of claim 10, wherein determining, for each of a plurality of pressures, the density, the speed of sound, and the heat capacity of the sample comprises numerically integrating the density, the speed of sound over at least a subset of the plurality of pressures.

### Claim 16 (depends on 15)

The method of claim 15, wherein the numerically integrating comprises:
determining, at a first pressure the derivative with respect to pressure of the density and the derivative with respect to pressure of the specific heat; and
estimating, at a second pressure, the density and the specific heat at a greater pressure based at least in part on the density, the specific heat, and the derivatives.

### Claim 17 (depends on 10)

The method of claim 10, wherein determining, for each of a plurality of pressures, the density, the speed of sound, and the heat capacity of the sample comprises representing the density, the speed of sound, and the heat capacity as polynomial functions with rational exponents.

### Claim 18 (depends on 17)

The method of claim 17, wherein determining, for each of a plurality of pressures, the density, the speed of sound, and the heat capacity of the sample comprises determining one or more parameters of the polynomial functions based at least in part on regression analysis.

### Claim 19

A system, comprising:
means for pressurizing and depressurizing a fluid;
means for measuring a compressibility of the fluid, wherein the compressibility comprises an isothermal compressibility κT or an isentropic compressibility κS, wherein the isothermal compressibility is defined by the equation
κ
T
=
-
1
V
⁢
(
∂
V
∂
p
)
T
and the isentropic compressibility is defined by the equation
κ
S
=
-
1
V
⁢
(
∂
V
∂
p
)
S
where V is volume, p is pressure, S is entropy, and T is temperature;
means for measuring a speed of sound of the fluid; and
means for determining, based at least in part on the speed of sound and a density of the fluid calculated based on the compressibility and the speed of sound, one or more of a heat capacity of the fluid, an expansivity of the fluid, or an adiabatic index of the fluid.